Simplify to lowest terms. $\dfrac{18}{63}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 18 and 63? $18 = 2\cdot3\cdot3$ $63 = 3\cdot3\cdot7$ $\mbox{GCD}(18, 63) = 3\cdot3 = 9$ $\dfrac{18}{63} = \dfrac{2 \cdot 9}{ 7\cdot 9}$ $\hphantom{\dfrac{18}{63}} = \dfrac{2}{7} \cdot \dfrac{9}{9}$ $\hphantom{\dfrac{18}{63}} = \dfrac{2}{7} \cdot 1$ $\hphantom{\dfrac{18}{63}} = \dfrac{2}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{18}{63}= \dfrac{3\cdot6}{3\cdot21}= \dfrac{3\cdot 3\cdot2}{3\cdot 3\cdot7}= \dfrac{2}{7}$